These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 23. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/23, 1/23, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 9/1, 11/1, 12/1, 14/1 15/1, 17/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.138725) (-0.138160,-0.093930) (-0.092666,-0.089218) (-0.086228,-0.085207) (-0.081541,-0.080627) (-0.078177,-0.075709) (-0.073545,-0.072800) (-0.070107,-0.069431) (-0.067606,-0.065753) (-0.064114,-0.063548) (-0.061486,-0.060965) (-0.059554,-0.058111) (-0.053216,-0.052060) (-0.048097,-0.047151) (-0.043876,-0.043088) (-0.040336,-0.039669) (-0.037325,-0.036753) (-0.034732,-0.034237) (-0.032477,-0.032043) (-0.030496,-0.030113) (-0.028743,-0.028402) (-0.027180,-0.026876) (-0.025779,-0.025505) (-0.024515,-0.024267) (-0.023369,-0.023144) (-0.022326,-0.022120) (-0.021371,-0.021183) (-0.020495,-0.020322) ( 0.020322,0.020495 ) ( 0.021183,0.021371 ) ( 0.022120,0.022326 ) ( 0.023144,0.023369 ) ( 0.024267,0.024515 ) ( 0.025505,0.025779 ) ( 0.026876,0.027180 ) ( 0.028402,0.028743 ) ( 0.030113,0.030496 ) ( 0.032043,0.032477 ) ( 0.034237,0.034732 ) ( 0.036753,0.037325 ) ( 0.039669,0.040336 ) ( 0.043088,0.043876 ) ( 0.047151,0.048097 ) ( 0.052060,0.053216 ) ( 0.058111,0.059554 ) ( 0.060965,0.061486 ) ( 0.063548,0.064114 ) ( 0.065753,0.067606 ) ( 0.069431,0.070107 ) ( 0.072800,0.073545 ) ( 0.075709,0.078177 ) ( 0.080627,0.081541 ) ( 0.085207,0.086228 ) ( 0.089218,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-0.138907,-0.138019) -9/65 HST (-0.098076,-0.088511) -3/32 EXTENDED HST -> HST (-0.088561,-0.088310) -10/113 HST (-0.088349,-0.088262) -37/419 HST (-0.088602,-0.087919) -100/1133 HST (-0.088259,-0.088212) -3/34 EXTENDED HST (-0.088041,-0.087400) -5/57 HST (-0.091243,-0.083499) -9/103 HST (-0.086991,-0.086922) -2/23 EXTENDED HST (-0.083529,-0.083461) -43/515 HST (-0.083486,-0.083433) -55/659 HST (-0.083860,-0.083002) -70/839 HST (-0.083396,-0.083270) -1/12 EXTENDED HST (-0.087902,-0.075909) -4/49 EXTENDED HST -> HST (-0.079575,-0.070944) -4/53 HST (-0.075017,-0.074983) -3/40 EXTENDED HST (-0.074099,-0.074049) -2/27 EXTENDED HST (-0.075630,-0.065123) -4/57 HST (-0.067640,-0.062544) -14/215 HST (-0.065111,-0.064760) -5/77 HST (-0.064535,-0.064497) -2/31 EXTENDED HST (-0.062553,-0.062535) -89/1423 HST (-0.062535,-0.062465) -1/16 EXTENDED HST (-0.066364,-0.057020) -4/65 HST (-0.061250,-0.052730) -13/228 HST (-0.057007,-0.056814) -7/123 HST (-0.056827,-0.056382) -3/53 HST (-0.055584,-0.055528) -1/18 EXTENDED HST (-0.054856,-0.048838) -4/77 HST (-0.051732,-0.051716) -3/58 EXTENDED HST (-0.051294,-0.051270) -2/39 EXTENDED HST (-0.050023,-0.049977) -1/20 EXTENDED HST (-0.050847,-0.046809) -21/430 HST (-0.048791,-0.048770) -2/41 EXTENDED HST (-0.046820,-0.046638) -5/107 HST (-0.048740,-0.044519) -9/193 HST (-0.046521,-0.046502) -2/43 EXTENDED HST (-0.045473,-0.045436) -1/22 EXTENDED HST (-0.044538,-0.044483) -15/337 HST (-0.045122,-0.043839) -27/607 HST (-0.044453,-0.044435) -2/45 EXTENDED HST (-0.045445,-0.040438) -4/93 HST (-0.042863,-0.042852) -3/70 EXTENDED HST (-0.042561,-0.042545) -2/47 EXTENDED HST (-0.041682,-0.041651) -1/24 EXTENDED HST (-0.040454,-0.040409) -15/371 HST (-0.040589,-0.040227) -91/2252 HST (-0.040408,-0.040400) -4/99 EXTENDED HST (-0.041855,-0.037236) -4/101 HST (-0.039478,-0.039469) -3/76 EXTENDED HST (-0.039223,-0.039209) -2/51 EXTENDED HST (-0.038475,-0.038448) -1/26 EXTENDED HST (-0.038790,-0.034503) -4/109 HST (-0.036589,-0.036581) -3/82 EXTENDED HST (-0.036370,-0.036358) -2/55 EXTENDED HST (-0.035726,-0.035703) -1/28 EXTENDED HST (-0.036144,-0.032145) -4/117 HST (-0.034094,-0.034087) -3/88 EXTENDED HST (-0.033904,-0.033893) -2/59 EXTENDED HST (-0.033343,-0.033323) -1/30 EXTENDED HST (-0.033835,-0.030088) -4/125 HST (-0.031918,-0.031912) -3/94 EXTENDED HST (-0.031751,-0.031741) -2/63 EXTENDED HST (-0.031259,-0.031241) -1/32 EXTENDED HST (-0.031804,-0.028278) -4/133 HST (-0.030003,-0.029997) -3/100 EXTENDED HST (-0.029855,-0.029847) -2/67 EXTENDED HST (-0.029420,-0.029404) -1/34 EXTENDED HST (-0.028282,-0.028215) -5/177 HST (-0.029501,-0.026923) -9/319 HST (-0.028173,-0.028165) -2/71 EXTENDED HST (-0.027785,-0.027771) -1/36 EXTENDED HST (-0.028395,-0.025242) -4/149 HST (-0.026788,-0.026784) -3/112 EXTENDED HST (-0.026670,-0.026663) -2/75 EXTENDED HST (-0.026322,-0.026310) -1/38 EXTENDED HST (-0.025254,-0.025166) -3/119 HST (-0.027193,-0.023054) -4/159 HST (-0.025006,-0.024994) -1/40 EXTENDED HST (-0.023064,-0.023019) -5/217 HST (-0.024072,-0.021963) -9/391 HST (-0.022991,-0.022986) -2/87 EXTENDED HST (-0.022732,-0.022723) -1/44 EXTENDED HST (-0.023611,-0.020300) -13/592 HST (-0.021958,-0.021929) -7/319 HST (-0.021931,-0.021865) -3/137 HST (-0.021743,-0.021735) -1/46 EXTENDED HST (-0.080056,0.095345 ) 0/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,d,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c>(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "a*b*c*d");